SSDT is now the BIDS client tool for working with Business Intelligence projects with SQL Server. You can download SSDT from here that includes support for SQL Server 2014 as well.

Once you have that installed you can work with the projects from within the SSDT environment, you just would not be able to deploy the projects to an actual SQL Server instance. The services (or components) do not exist with the SQL Server Express Edition. You would just execute your projects from within SSDT. I believe most books or tutorials you work through to get familiar with SSIS task and building of actual packages will work with just SSDT and a database in Express Edition. The only thing lacking would be the deployment process itself. This is the type of environment I generally use for development and general testing of certain things with SSIS or SSRS.

If you would like to also work on having the projects deployed and run within an environment or instance of SQL Server similar to a real production system then I would suggest purchasing a developer license. The developer edition is same functionality and features of Enterprise Edition. This will provide the components for SSIS, SSRS, and SSAS (the services that execute or run the packages/files). General cost of Developer Edition is about $50 (U.S.).

What I read on internet is this: "SQL Server Data Tools (SSDT) is a toolset which provides an integrated environment for database developers to carry out all their database design work for any SQL Server platform (both on and off premise) within Visual Studio. Database developers can use the SQL Server Object Explorer in VS to easily create or edit database objects and data, or execute queries."

But what is not clear to me is: if I haven't installed a SQL Server engine (e.g. SQL Server 2012), how to and where SSDT run/execute DDL/DML queries and store my .mdf file??

What I want ask to you is: Do SSDT is only a client tool or it provide also a server engine for run/execute DDL/DML queries and store my .mdf file??